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svetlana [45]
3 years ago
9

Please Help !!! its a math problem What is the range of the quadratic equation whose graph contains the following points?

Mathematics
1 answer:
dolphi86 [110]3 years ago
4 0
<h2>Range of a Quadratic Function</h2>

The range tells us the possible <em>y</em>-values that occur in the function.

When describing the range, we can write an inequality using <em>y</em>.

  • Examples: y > 6, y ≤ 10

When describing the range of a quadratic function, we typically use the ≥ or ≤ symbols when writing the inequality.

To write the range of a quadratic function,

  1. Find the vertex
  2. Determine whether the parabola opens up or down
  3. Set <em>y</em> ≥ or ≤ the y-coordinate of the vertex

<h2>Solving the Question</h2>

We're given:

  • Vertex at (0,4)
  • Other points on the graph: (-2,0), (-1,3), (1,3), (2,0)

Because we're directly given the vertex, we just have to determine now whether the parabola opens up or down.

  • If the other points on the graph always have a lower <em>y-</em>coordinate value, then the graph opens down
  • If the other points on the graph always have a greater <em>y-</em>coordinate value, then the graph opens up

The other points that fall on the graph that we're given all have a lower y-coordinate value than 4, that means this parabola opens down.

Therefore, all other y-values for the function will be less than 4.

Therefore, y ≤ 4.

<h2>Answer</h2>

y ≤ 4

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